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What is the length of the line x plus y equals 7 that spans the curve x2 plus y2 equals 25?
Wiki User
∙ 6y ago
If: x +y = 7 then y = 7 -x
IF: x^2 +y^2 = 25 then x^2 +(7 -x)^2 -25 = 0
Removing brackets: x^2 +49 -14x +x^2 -25 = 0
Collecting like terms: 2x^2 -14x +24 = 0
Dividing all terms by 2: x^2 -7x +12 = 0
Factorizing: (x -3)(x -4) = 0 => x = 3 or x = 4
By substitution points of intersection are at: (3, 4) and (4, 3)
Using distance formula: length of line from (3, 4) to (4, 3) = square root of 2
Wiki User
∙ 6y ago
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What is the length of the line x -y equals 2 that spans the curve x squared - 4y squared equals 5?
The line x-y = 2 intersects with the curve x^2 -4y^2 = 5 at (2.5, 1/3) and (3, 1) and by using the distance formula its length is 5/6
What is the length of the line x -2y equals 8 that spans the curve xy equals 24 showing work?
If: x-2y = 8 and xy = 24 Then: x = 8+2y and y(8+2y) = 24 => 2y^2+8y-24 = 0 Solving the above quadratic equation: y = 2 or y = -6 Points of intersection of the line with the curve: (-4, -6) and (12, 2) Length of line: square root [(-4-12)^2 plus (-6-2)^2] = square root of 320 which is about 18 units rounded to the nearest integer
What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
What is the length of the line y equals 5x plus 10 that meets the curve of y equals x squared plus 4 at two distinctive points?
The line of y = 5x+10 intersects with the curve of y = x2+4 at (6, 40) and (-1, 5) Length of the line is the square root of: (6--1)2+(40-5)2 = 7 times sq rt of 26 or 35.693 to three decimal places
What is the length of the line y equals 8 -x that meets the curve of y equals x squared plus 4x plus 2 at two distinctive points?
7*sqrt(2) = 9.899 to 3 dp
What is the length of the line x -y equals 2 that spans the curve x squared - 4y squared equals 5?
The line x-y = 2 intersects with the curve x^2 -4y^2 = 5 at (2.5, 1/3) and (3, 1) and by using the distance formula its length is 5/6
What is the length of the line of y equals 17 -3x that spans the curve of y equals x squared plus 2x -7?
If you mean: y = 17-3x and y = x^2+2x-7 then the length of the line works out as 11 times square root of 10 or about 34.785 to three decimal places.
What is the length of the line x -2y equals 8 that spans the curve xy equals 24 showing work?
If: x-2y = 8 and xy = 24 Then: x = 8+2y and y(8+2y) = 24 => 2y^2+8y-24 = 0 Solving the above quadratic equation: y = 2 or y = -6 Points of intersection of the line with the curve: (-4, -6) and (12, 2) Length of line: square root [(-4-12)^2 plus (-6-2)^2] = square root of 320 which is about 18 units rounded to the nearest integer
What is the length of the line that spans the parabolas of y equals 4x squared -2x -1 and y equals -2x squared plus 3x plus 5?
If: y = 4x2-2x-1 and y = -2x2+3x+5 Then the length of the line works out as: 65/18 or 3.6111 ... recurring decimal 1
How do you calculate the length of the curve using calculus?
Do a line integral.
What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
What is the length of the line y equals 5x plus 10 that meets the curve of y equals x squared plus 4 at two distinctive points?
The line of y = 5x+10 intersects with the curve of y = x2+4 at (6, 40) and (-1, 5) Length of the line is the square root of: (6--1)2+(40-5)2 = 7 times sq rt of 26 or 35.693 to three decimal places
What is the length of the line y equals 8 -x that meets the curve of y equals x squared plus 4x plus 2 at two distinctive points?
7*sqrt(2) = 9.899 to 3 dp
What is the point of cotact when the line y equals 2x plus 5 over 4 meets the curve y squared equals 10xa?
If you mean a line of y = 2x+5/4 and a curve of y^2 = 10x Then it works out that the line touches the curve at: (5/8, 5/2)
What is the value of k when y equals 3x plus 1 is a line tangent to the curve of x squared plus y squared equals k hence finding the point of contact of the line to the curve?
It is (-0.3, 0.1)
What is tangent line?
tan A = (sin A) / (cos A) tan (A)= opposite side length/adjacent side length A is an angle measurement; amount of degrees or radians. If a line is tangent to a curve, it only touches the curve at one point. looks like )| but the line is touching the curve. In a circle, the tangent line touches the circle at one point and is perpinducular to the circle's radius if it is touching that same point.
What is the path to a moving point having length but no breadth in mathematics?
A line, or more generally, a curve.
